Pieces and method for producing multiple forms of a three-dimensional construction game

ABSTRACT

An invention and method for producing ttetragonal prism shaped puzzle pieces that may have on their rectangular faces cubic projections. The pieces are grouped according to the volume of the tetragonal prism, which can have a stack of five, four, three, two or one cubic projection(s). The pieces are further differentiated according to the number of rectangular faces with cubic projections and their arrangement. A production method for making a wide variety of geometric or irregular objects consists of selecting pieces, repeated if necessary, and assembling the pieces into the form of a desired object. Then the pieces forming the periphery of the desired object are cut from the assembly of pieces. This provides the base pattern for the pieces necessary to make the desired object. Thereafter, mechanisation of the pieces allows for mass production of a wide variety of three-dimensional puzzles with interior pieces and detailed exterior form.

CROSS-REFERENCE TO RELATED APPLICATIONS

This is a PCT National Stage Application. Priority is claimed from foreign (Spain) application ES 200201373 U (WIPO WO 03101559), May 29, 2002.

BACKGROUND

The present version of the invention is generally related to pieces for three-dimensional construction games. Construction games, jigsaws and 3-D puzzles are included within this category.

Traditionally in this field there are jigsaw puzzle pieces which are constructed by assembling pieces that in turn can be used to produce geometric shapes: cubes, stars, pyramids, spheres, etc (normally geometric or regular shapes). There are also “3D-puzzles”, which consist of pieces similar to those of flat puzzles, but sturdier and, when assembled, reproduce the surface of a three-dimensional figure. Generally, these puzzles have no pieces on the inside. There are also puzzle pieces that belong to so called “construction games”, which can fit together and can lead to reproductions of three-dimensional figures (irregular or geometric), with a certain approximation of their outline.

These puzzles and their related pieces do not have interior pieces as well as exterior ones. Also, these puzzles do not provide for representation of a constructed irregular object with precision in the outline and shape.

SUMMARY

The present version of the invention is directed to pieces and a method capable of reproducing by means of assembling three-dimensional pieces, a great variety of three-dimensional shapes (not just geometric) with interior pieces as well as exterior ones and with precision in the outline of the constructed object.

The disclosure describes a version of the invention made up of 27 pieces that are tetragonal prisms with cubic projections on the rectangular faces of each prism. When these pieces are chosen (using repetition of pieces, as necessary), assembled and fitted together, the pieces form multiple objects, like cubes, tetragonal prisms, and staggered pyramids.

The disclosure also describes a manufacturing process for mechanizing the construction of the pieces to be assembled. First pieces are combined and put together to form the body of the desired shape. The pieces of the assembly are cut to reproduce the surface of the solid three-dimensional shape. The result is a three-dimensional puzzle (geometric or irregularly shaped) with i) three-dimensional pieces ii) a detailed outline of the desired exterior shape and iii) with interior pieces.

The pieces are formed in the shape of tetragonal prisms with cubic projections on their rectangular faces. The volume of the tetragonal prism can be used to differentiate between different groupings of pieces. For example, the cubic extensions, or cubes, that form the backbone of the tetragonal prism (“cubeoid”) may have a volume equivalent to the superposition of 5, 4, 3, 2, or 1 cubic extension(s) (i.e., cubes).

Within these five groups, the pieces are differentiated by the number of cubic projections (cubes) on the available rectangular faces of the cubeoid. There can be cubes on 4 of the rectangular faces of the cubeoid; on 3 of the rectangular faces of the cubeoid; on 2 of the adjacent faces of the cubeoid; on 2 of the non-adjacent faces of the cubeoid; on 1 of the faces of cubeoid or none. The cubic extensions (i.e., cubes) are placed symmetrically on the different rectangular faces in a way so that the cubic extensions (i.e., cubes) are all situated at the same height on the tetragonal prism.

This means that the cubic projections of one piece fit together with the empty spaces between the cubic projections of another piece, and so when the pieces are put together, the pieces form compact and cohesive shapes.

DETAILED DESCRIPTION OF THE DRAWINGS

These and other features, aspects, and advantages of the present version of the invention will become better understood with regard to the following description, appended claims, and accompanying drawings where:

FIG. 1 is a tetragonal prism (31) that is a cubeoid of five cubes and is designated as being the 1 piece.

FIG. 2 is a tetragonal prism (32) of equal volume to piece 1, with two cubic projections (33 and 34) situated in one of its rectangular faces and is designated as the 2 piece.

FIG. 3 is a tetragonal prism (35) of equal volume to pieces 1 and 2 with two pairs of cubic projections situated respectively in two of its adjacent rectangular faces (36, 37, 39 and 39), and is designated as being the 3 piece.

FIG. 4 is a tetragonal prism (40) of equal volume to shapes 1, 2 and 3, with three pairs of cubic projections situated respectively in three of its rectangular faces (41, 42, 43, 44, 45, and 46), and is designated in the described version of the invention as being the 4 piece.

FIG. 5 is a tetragonal prism (47) of equal volume to shapes 1, 2, 3 and 4, with two pairs of cubic projections (48, 49, 50 and 51) situated respectively side by side two of its non-adjacent rectangular faces, and is designated in the described version of the invention as being the 5 piece

FIG. 6 is a tetragonal prism (52) of equal volume to shapes 1, 2, 3, 4 and 5, with four pairs of cubic projections (53, 54, 55, 56; 57, 58, 59 and 60) situated respectively on its four rectangular faces, and is designated in the described version of the invention as being the 6 piece

FIG. 7 is a tetragonal prism (61) of equal volume to the superposition of four cubic projections, and is designated in the described version of the invention as being the 7 piece

FIG. 8 is a tetragonal prism (62) of equal volume to shape 7 with two cubic projections (63 and 64) situated on one of its rectangular faces and is designated in the described version of the invention as being the 8 piece

FIG. 9 is a tetragonal prism (65) of equal volume to shapes 7 and 8, with two pairs of cubic projections (66 and 67; 68 and 69) situated respectively on two of its adjacent rectangular faces, and is designated in the described version of the invention as being the 9 piece

FIG. 10 is a tetragonal prism (70) of equal volume to shapes 7, 8 and 9, with two pairs of cubic projections (71 and 72; 73 and 74) situated respectively on two of its non-adjacent rectangular faces, and is designated in the described version of the invention as being the 10 piece

FIG. 11 is a tetragonal prism (75) of equal volume to shapes 7, 8, 9 and 10, with three pairs of cubic projections (76 and 77, 78 and 79, 80 and 51), situated respectively on three of its rectangular faces, and is designated in the described version of the invention as being the 11 piece

FIG. 12 is a tetragonal prism (82) of equal volume to shapes 7, 8, 9, 10 and 11, with a pair of cubic projections (83, 84, 85, 86, 87, 88, 89 and 90) on each of its four rectangular faces, and is designated in the described version of the invention as being the 12 piece

FIG. 13 is a tetragonal prism (91) of equal volume to the superposition of three cubic projections, and is designated in the described version of the invention as being the 13 piece

FIG. 14 is a tetragonal prism (92) of equal volume to shape 13 with two cubic projections (93 and 94) situated in one of its rectangular faces, and is designated in the described version of the invention as being the 14 piece

FIG. 15 is a tetragonal prism (95) of equal volume to shapes 13 and 14, with two pairs of cubic projections (96, 97, 98 and 99) situated respectively on two of its adjacent rectangular faces, and is designated in the described version of the invention as being the 15 piece

FIG. 16 is a tetragonal prism (100) of equal volume to shapes 13, 14 and 15, with two pairs of cubic projections (101, 102, 103 and 104) situated respectively on two of its non-adjacent rectangular faces, and is designated in the described version of the invention as being the 16 piece

FIG. 17 is a tetragonal prism (112) of equal volume to shapes 13, 14, 15 and 16, with three pairs of cubic projections (106, 107, 108, 109, 110 and 111) situated respectively on three of its rectangular faces, and is designated in the described version of the invention as being the 17 piece

FIG. 18 is a tetragonal prism (112) of equal volume to shapes 13, 14, 15, 16 and 17, with four pairs of cubic projections (113, 114, 115, 116, 117, 118, 119 and 120) situated respectively on its four rectangular faces, and is designated in the described version of the invention as being the 18 piece

FIG. 19 is a tetragonal prism (1121) of equal volume to shapes 13, 14, 15, 16, 17 and 18, with four cubic projections (122, 123, 124 and 125) situated respectively on its four rectangular faces, and is designated in the described version of the invention as being the 19 piece

FIG. 20 is a tetragonal prism (126) of equal volume to shape 19, with three cubic projections (127, 128 and 129) situated respectively on three of its rectangular faces, and is designated in the described version of the invention as being the 20 piece

FIG. 21 is a tetragonal prism (130) of equal volume to shapes 19 and 20, with two cubic projections (131 and 132) situated respectively on two of its adjacent rectangular faces, and is designated in the described version of the invention as being the 21 piece

FIG. 22 is a tetragonal prism (133) of equal volume to shapes 19, 20 and 21, with two cubic projections (134, 135) situated respectively on two of its non-adjacent faces, and is designated in the described version of the invention as being the 22 piece

FIG. 23 is a tetragonal prism (136) of equal volume to shapes 19, 20, 21 and 22, with a cubic projection (137) situated on one of its rectangular faces, and is designated in the described version of the invention as being this the 23 piece

FIG. 24 is a tetragonal prism (142) of equal volume to the superposition of two cubic projections, and is designated in the described version of the invention as being this the 24 piece

FIG. 25 is a tetragonal prism (142) of equal volume to shape 24 with a cubic projection (143) situated on one of his rectangular faces, and is designated in the described version of the invention as being the 25 piece

FIG. 26 is a tetragonal prism (139) of equal volume to shapes 24 and 25, with two cubic projections (140 and 141) situated respectively on two of its adjacent rectangular faces, and is designated in the described version of the invention as being the 26 piece

FIG. 27 is a cube (144) of equal volume to a cubic projection, and is designated in the described version of the invention as being the 27 piece

FIG. 28 is a cube made from the assembling of various pieces: six 2 pieces, eight 3 pieces, nine 4 pieces, eight 5 pieces, two 6 pieces, seven 8 pieces, fifteen 9 pieces, two 10 pieces, six 11 pieces, two 12 pieces, nine 14 pieces, seven 15 pieces, five 16 pieces, one 17 piece, two 24 pieces, two 25 pieces and one 26 piece.

FIG. 29: The six faces of the same cube in FIG. 28 laid out flat

FIG. 30: The result of processing the pieces from the same cube of FIG. 28 or FIG. 29 to produce the form of a triangular based prism.

DETAILED DESCRIPTION

The current version of the described version of the invention is 27 pieces that are tetragonal prisms with cubic projections on the rectangular faces of each prism. When these pieces are assembled and fitted together, they form multiple shapes, such as cubes, tetragonal prisms, and staggered pyramids.

The 27 pieces that are tetragonal prisms have one to thirteen equal cubes. Each of the tetragonal prisms has a backbone of one or more equal cubes, hereinafter called a “cubeoid.” The cubeoid of a tetragonal prism is one of the subsets of five equal cubes:

-   -   a) a stack of five equal cubes (1, 2, 3, 4, 5 and 6);     -   b) a stack of four equal cubes (7, 8, 9, 10, 11 and 12);     -   c) a stack of three equal cubes (13, 14, 15, 16, 17, 18, 19, 20,         21, 22 and 23);     -   d) a stack of two equal cubes (24, 25 and 26) or;     -   e) one (27) cube.

Furthermore, the tetragonal prism is further categorized into one of six possible sub-groups defined by the possible arrangement of cubes on the four sides (excluding the top and bottom side) of the cubeoid:

-   -   a) all four sides have additional cubes (6, 12, 18, 19),     -   b) three sides have additional cubes (4, 11, 17, 20),     -   c) two adjacent sides have additional cubes (3, 9, 15, 21, 26),     -   d) two non-adjacent sides have additional cubes (5, 10, 16, 22),     -   e) one side has additional cubes (2, 8, 14, 23, 25), or     -   f) no side has additional cubes (1, 7, 13, 24, 27).

Another way to describe the sub-grouping of pieces is that within the five primary groups, the pieces are differentiated by the number of rectangular faces on the tetragonal prism that have cubic projections. The number of faces that have cubic projections can be 4 (pieces 6, 12, 18, 19); 3 (pieces 4, 11, 17, 20); 2 adjacent faces (pieces 3, 9, 15, 21, 26); 2 non-adjacent (pieces 5, 10, 16, 22); 1 (pieces 2, 8, 14, 23, 25); or none (1, 7, 13, 24, 27).

The cubic projections, or cubes, on the rectangular faces of the cubeoid are placed symmetrically. This means that the cubic projections on the different rectangular faces are all situated at the same height on the tetragonal prism.

A tetragonal prism with two cubes on any of the rectangular sides of the cubeoid has space equal to the volume of a single cube between the two cubes; and therefore, a tetragonal prism with two cubes on any one side of the cubeoid can have the two cubes at the height of the second and fourth cubes of the cubeoid (1, 2, 3, 4, 5 and 6); or at the height of the first and third cube in the cubeoid (7, 8, 9, 10, 11, 12, 14, 15, 16, 17, 18);

When the tetragonal prism has one cube on a side of the cubeoid, the cube can be placed at the height of the second cube in the cubeoid (19, 20, 21, 22, and 23) or at the height of the first cube in the cubeoid (25, 26). When the cubeoid comprises two cubes, the tetragonal prism can have one cube on one side of the tetragonal prism (25) or two cubes on two adjacent sides of the tetragonal prism, each cube on one side at the height of the first cube in the cubeoid (26). Or the cubeoid can comprise one cube (FIG. 27).

The cubic projections of one piece fit together in the empty spaces between the cubic projections of another piece, and so when the pieces are put together, the pieces form compact and cohesive shapes.

One example of putting the pieces together is a cube (FIG. 28), the volume of which is equivalent to 9×9×9 cubic projections made by assembling the group of pieces, with repetition of pieces: the 2 piece, the 3 piece, the 4 piece, the 5 piece, the 6 piece, the 7 piece, the 8 piece, the 9 piece, the 10 piece, the 11 piece, the 12 piece, the 14 piece, the 15 piece, the 16 piece, the 17 piece, the 23 piece, the 24 piece, the 25 piece and the 26 piece.

Other examples include:

-   -   a. Two 26 pieces can make a cube of 2×2×2.     -   b. A 16 piece, a 17 piece and an 18 piece can make a cube of         3×3×3.     -   c. Two 11 pieces, one 12 piece, one 10 piece and four 8 pieces         can make a cube of 4×4×4.     -   d. Nine 2 pieces, one 3 piece, two 5 pieces, one 6 pieces and         two 4 pieces can make a cube of 5×5×5 . . .     -   e. One 10 piece, one 15 piece, six 2 pieces, two 5 pieces, four         4 pieces, two 3 pieces, two 6 pieces, three 8 pieces, four 14         pieces, one 16 piece, one 22 piece and one 25 piece can make a         cube of 6×6×6

Once put together, the pieces reproduce a three-dimensional shape. It is possible to form many different three-dimensional shapes from the pieces. The three-dimensional shapes may have interior and exterior pieces. So it is possible to reproduce a great variety of three-dimensional shapes which might be, for example, cubes, tetragonal prisms, or staggered pyramids. It is also possible to reproduce a great variety of three-dimensional objects, geometric or irregular, after mechanization of some of the constituent pieces.

Piece 1 is a tetragonal prism (31) comprising a stack of five equal cubes.

Piece 2 is a tetragonal prism (32) comprising a stack of five equal cubes with equal cubes placed on one of the rectangular faces of the said stack at the height of the second cube of the said stack (34) and at the height of the fourth cube (33) of the said stack.

Piece 3 is a tetragonal prism (35) comprising a stack of five equal cubes with equal cubes placed on two of the adjacent rectangular faces of said stack at the height of the second cube in said stack (37 and 39) and the fourth cube in said stack (36 and 38).

Piece 4 is a tetragonal prism (40) comprising a stack of five equal cubes with three pairs of equal cubes placed on three of rectangular faces of said stack at the height of the second cube in said stack (42, 44 and 46) and the fourth cube in said stack (41, 43 and 45).

Piece 5 is a tetragonal prism (47) comprising a stack of five equal cubes with two pairs of equal cubes placed on two of the non-adjacent rectangular faces of said stack at the height of the second cube in said stack (49 and 51) and the fourth cube in said stack (48 and 50).

Piece 6 is a tetragonal prism (52) comprising a stack of five equal cubes with four pairs of equal cubes on four rectangular faces of said stack at the height of the second cube in said stack (54, 56, 58 and 60) and the fourth cube in said stack (53, 55, 57 and 59).

Piece 7 is a tetragonal prism comprising a stack of four equal cubes (61).

Piece 8 is a tetragonal prism (62) comprising a stack of four equal cubes with two equal cubes on one of the rectangular faces of said stack at the height of the first cube in said stack (64) and the third cube in said stack (63).

Piece 9 is a tetragonal prism (65) comprising a stack of four equal cubes with two pairs of equal cubes on two adjacent rectangular faces of said stack at the height of the first cube in said stack (67 and 69) and the third cube in said stack (66 and 68).

Piece 10 is a tetragonal prism (70) comprising a stack of four equal cubes with two pairs of equal cubes placed on two non-adjacent rectangular faces of said stack at the height of the first cube in said stack (72 and 74) and the third cube in said stack (71 and 73).

Piece 11 piece is a tetragonal prism (75) comprising a stack of four equal cubes with three pairs of equal cubes placed on three of the rectangular faces of said stack at the height of the first cube of said stack (77, 79 and 81) and the third cube of said stack (76, 78 and 80).

Piece 12 piece is a tetragonal prism (82) comprising a stack of four equal cubes with four pairs of equal cubes placed on the four rectangular faces of said stack at the height of the first cube in said stack (84, 86, 88 and 90) and the third cube of said stack (83, 85, 87 and 89).

Piece 13 piece is a tetragonal prism (91) comprising a stack of three equal cubes.

Piece 14 is a tetragonal prism (92) comprising a stack of three equal cubes with two equal cubes placed on one of the rectangular faces of said stack at the height of the first cube in said stack (94) and the third cube in said stack (93).

Piece 15 is a tetragonal prism (95) comprising a stack of three equal cubes with two pairs of equal cubes placed on two of the adjacent rectangular faces of said stack at the height of the first cube in said stack (97 and 99) and the third cube in said stack (96 and 98).

Piece 16 is a tetragonal prism (100) comprising a stack of three equal cubes with two pairs of equal cubes placed on two of the non-adjacent rectangular faces of said stack at the height of the first cube in said stack (102 and 104) and the third cube of said stack (101 and 103).

Piece 17 is a tetragonal prism (105) comprising a stack of three equal cubes with three pairs of equal cubes placed on three of the rectangular faces of said stack at the height of the first cube in the said stack (107, 109 and 111) and the third cube in the said stack (106, 108 and 110).

Piece 18 is a tetragonal prism (112) comprising a stack of three equal cubes with four pairs of equal cubes placed on the four rectangular faces of said stack at the height of the first cube in the said stack (114, 116, 118 and 120) and the third cube in said stack (113, 115, 117 and 119).

Piece 19 is a tetragonal prism (121) comprising a stack of three equal cubes with four equal cubes placed on the four rectangular faces of said stack at the height of the second cube in said stack (122, 123, 124 and 125).

Piece 20 is a tetragonal prism (126) comprising a stack of three equal cubes with three equal cubes placed on three of the rectangular faces of said stack at the height of the second cube in said stack (127, 128 and 129).

Piece 21 is a tetragonal prism (130) comprising a stack of three equal cubes with two equal cubes placed on two of the adjacent rectangular faces of said stack at the height of the second cube in said stack (131 and 132).

Piece 22 is a tetragonal prism (133) comprising a stack of three equal cubes with two equal cubes placed on two of the non-adjacent rectangular faces at the height of the second cube in said stack (134 and 135).

Piece 23 is a tetragonal prism (136) comprising a stack of three equal cubes with one equal cube placed on one of the rectangular faces of said stack at the height of the second cube in said stack (137).

Piece 24 is a tetragonal prism (138) comprising a stack of two equal cubes.

Piece 25 is a tetragonal prism (142) comprising a stack of two equal cubes with one equal cube (143) placed on one of the rectangular faces of said stack at the height of the first cube in said stack.

Piece 26 is a tetragonal prism (139) comprising a stack of two equal cubes with two equal cubes (140 and 141) placed on two of the adjacent rectangular faces of said stack at the height of the first cube in said stack.

Piece 27 is a tetragonal prism (144) with a volume of one equal cube.

Various materials may be used, such as plastic and wood.

The pieces may be painted as well, with the colour of the paint being used to indicate the location of the puzzle piece. The exterior surface may be painted to match the colour and texture of a desired object, such as a building or car. The interior pieces may be painted with different colours, including one colour for each direction of the three-dimensional space.

The described version of the invention can further reproduce precise objects following a simple method. First, the 27 pieces can be made by way of moulding or machine tools. For example, machine tools are capable of height precision and producing complex geometry, (for example, in numerical control). Or the manufacturing process could make moulds of the 27 pieces, or a subset of the 27 pieces, that would be used to form the pieces of the selected object.

Upon completion of making the selected pieces, the selected pieces are assembled to match the desired object or an approximation. Once the results have been obtained by assembling the groups of said pieces, with repetitions of pieces, a desired shape may be obtained by cutting the pieces comprising the periphery of the assembled object. This reproduces a desired surface area for the desired three-dimensional object and the desired volume, integrated in the total volume, of the object (FIG. 29).

For example, suppose that one has a 9×9×9 cube (FIG. 28) and that one wants to make a prism with a triangular base from the pieces described. One can accomplish this as shown in FIG. 30 by cutting the pieces situated in the vertical plane of the diagonal of the base of the cube, as if one were cutting the cube along the plane which unites a top vertical edge with the opposite diagonal edge along the cube's base. 

1-26. (canceled)
 27. A three-dimensional construction game comprising 27 pieces that are tetragonal prisms of one to thirteen equal cubes.
 28. The three-dimensional construction game according to claim 27 wherein piece 1 is a tetragonal prism (31) comprising a stack of five equal cubes.
 29. The three-dimensional construction game according to claim 27 wherein piece 2 is a tetragonal prism (32) comprising a stack of five equal cubes with equal cubes placed on one of the rectangular faces of the said stack at the height of the second cube of the said stack (34) and at the height of the fourth cube (33) of the said stack.
 30. The three-dimensional construction game according to claim 27 wherein piece 3 is a tetragonal prism (35) comprising a stack of five equal cubes with equal cubes placed on two of the adjacent rectangular faces of said stack at the height of the second cube in said stack (37 and 39) and the fourth cube in said stack (36 and 38).
 31. The three-dimensional construction game according to claim 27 wherein piece 4 is a tetragonal prism (40) comprising a stack of five equal cubes with three pairs of equal cubes placed on three of rectangular faces of said stack at the height of the second cube in said stack (42, 44 and 46) and the fourth cube in said stack (41, 43 and 45).
 32. The three-dimensional construction game according to claim 27 wherein piece 5 is a tetragonal prism (47) comprising a stack of five equal cubes with two pairs of equal cubes placed on two of the non-adjacent rectangular faces of said stack at the height of the second cube in said stack (49 and 51) and the fourth cube in said stack (48 and 50).
 33. The three-dimensional construction game according to claim 27 wherein piece 6 is a tetragonal prism (52) comprising a stack of five equal cubes with four pairs of equal cubes on four rectangular faces of said stack at the height of the second cube in said stack (54, 56, 58 and 60) and the fourth cube in said stack (53, 55, 57 and 59).
 34. The three-dimensional construction game according to claim 27 wherein piece 7 is a tetragonal prism comprising a stack of four equal cubes (61).
 35. The three-dimensional construction game according to claim 27 wherein piece 8 is a tetragonal prism (62) comprising a stack of four equal cubes with two equal cubes on one of the rectangular faces of said stack at the height of the first cube in said stack (64) and the third cube in said stack (63).
 36. The three-dimensional construction game according to claim 27 wherein piece 9 is a tetragonal prism (65) comprising a stack of four equal cubes with two pairs of equal cubes on two adjacent rectangular faces of said stack at the height of the first cube in said stack (67 and 69) and the third cube in said stack (66 and 68).
 37. The three-dimensional construction game according to claim 27 wherein piece 10 is a tetragonal prism (70) comprising a stack of four equal cubes with two pairs of equal cubes placed on two non-adjacent rectangular faces of said stack at the height of the first cube in said stack (72 and 74) and the third cube in said stack (71 and 73).
 38. The three-dimensional construction game according to claim 27 wherein piece 11 is a tetragonal prism (75) comprising a stack of four equal cubes with three pairs of equal cubes placed on three of the rectangular faces of said stack at the height of the first cube of said stack (77, 79 and 81) and the third cube of said stack (76, 78 and 80).
 39. The three-dimensional construction game according to claim 27 wherein piece 12 is a tetragonal prism (82) comprising a stack of four equal cubes with four pairs of equal cubes placed on the four rectangular faces of said stack at the height of the first cube in said stack (84, 86, 88 and 90) and the third cube of said stack (83, 85, 87 and 89).
 40. The three-dimensional construction game according to claim 27 wherein piece 13 is a tetragonal prism (91) comprising a stack of three equal cubes.
 41. The three-dimensional construction game according to claim 27 wherein piece 14 is a tetragonal prism (92) comprising a stack of three equal cubes with two equal cubes placed on one of the rectangular faces of said stack at the height of the first cube in said stack (94) and the third cube in said stack (93).
 42. The three-dimensional construction game according to claim 27 wherein piece 15 is a tetragonal prism (95) comprising a stack of three equal cubes with two pairs of equal cubes placed on two of the adjacent rectangular faces of said stack at the height of the first cube in said stack (97 and 99) and the third cube in said stack (96 and 98).
 43. The three-dimensional construction game according to claim 27 wherein piece 16 is a tetragonal prism (100) comprising a stack of three equal cubes with two pairs of equal cubes placed on two of the non-adjacent rectangular faces of said stack at the height of the first cube in said stack (102 and 104) and the third cube of said stack (101 and 103).
 44. The three-dimensional construction game according to claim 27 wherein piece 17 is a tetragonal prism (105) comprising a stack of three equal cubes with three pairs of equal cubes placed on three of the rectangular faces of said stack at the height of the first cube in the said stack (107, 109 and 111) and the third cube in the said stack (106, 108 and 110).
 45. The three-dimensional construction game according to claim 27 wherein piece 18 is a tetragonal prism (112) comprising a stack of three equal cubes with four pairs of equal cubes placed on the four rectangular faces of said stack at the height of the first cube in the said stack (114, 116, 118 and 120) and the third cube in said stack (113, 115, 117 and 119).
 46. The three-dimensional construction game according to claim 27 wherein piece 19 is a tetragonal prism (121) comprising a stack of three equal cubes with four equal cubes placed on the four rectangular faces of said stack at the height of the second cube in said stack (122, 123, 124 and 125).
 47. The three-dimensional construction game according to claim 27 wherein piece 20 is a tetragonal prism (126) comprising a stack of three equal cubes with three equal cubes placed on three of the rectangular faces of said stack at the height of the second cube in said stack (127, 128 and 129).
 48. The three-dimensional construction game according to claim 27 wherein piece 21 is a tetragonal prism (130) comprising a stack of three equal cubes with two equal cubes placed on two of the adjacent rectangular faces of said stack at the height of the second cube in said stack (131 and 132).
 49. The three-dimensional construction game according to claim 27 wherein piece 22 is a tetragonal prism (133) comprising a stack of three equal cubes with two equal cubes placed on two of the non-adjacent rectangular faces at the height of the second cube in said stack (134 and 135).
 50. The three-dimensional construction game according to claim 27 wherein piece 23 is a tetragonal prism (136) comprising a stack of three equal cubes with one equal cube placed on one of the rectangular faces of said stack at the height of the second cube in said stack (137).
 51. The three-dimensional construction game according to claim 27 wherein piece 24 is a tetragonal prism (138) comprising a stack of two equal cubes.
 52. The three-dimensional construction game according to claim 27 wherein piece 25 is a tetragonal prism (142) comprising a stack of two equal cubes with one equal cube (143) placed on one of the rectangular faces of said stack at the height of the first cube in said stack.
 53. The three-dimensional construction game according to claim 27 wherein piece 26 is a tetragonal prism (139) comprising a stack of two equal cubes with two equal cubes (140 and 141) placed on two of the adjacent rectangular faces of said stack at the height of the first cube in said stack.
 54. The three-dimensional construction game according to claim 27 wherein piece 27 is a tetragonal prism (144) with a volume of one equal cube.
 55. The three-dimensional construction game according to claim 27 wherein the puzzle pieces are made from plastic.
 56. The three-dimensional construction game according to claim 27 wherein the puzzle pieces are made from wood.
 57. The three-dimensional construction game of claim 27 wherein each of the tetragonal prisms has a backbone of one or more equal cubes, hereinafter called a “cubeoid.”
 58. The tetragonal prism of claim 57 wherein the cubeoid comprises one of the subsets of five equal cubes, those subsets being: a) a stack of five equal cubes (1, 2, 3, 4, 5 and 6); b) a stack of four equal cubes (7, 8, 9, 10, 11 and 12); c) a stack of three equal cubes (13, 14, 15, 16, 17, 18, 19, 20, 21, 22 and 23); d) a stack of two equal cubes (24, 25 and 26) and; e) one (27) cube.
 59. The tetragonal prism of claim 58 wherein the tetragonal prism is comprised from one of six possible sub-groups defined by the possible arrangement of cubes on four faces of the cubeoid: a) all four sides have additional cubes (6, 12, 18, 19), b) three sides have additional cubes (4, 11, 17, 20), c) two adjacent sides have additional cubes (3, 9, 15, 21, 26), d) two non-adjacent sides have additional cubes (5, 10, 16, 22), e) one side has additional cubes (2, 8, 14, 23, 25), f) or no side has additional cubes (1, 7, 13, 24, 27).
 60. The tetragonal prism of claim 59 wherein said tetragonal prism has two cubes on any of the rectangular sides of the cubeoid with space equal to the volume of a single cube between the two cubes; and therefore, a tetragonal prism with two cubes on any one side of the cubeoid can have the two cubes at the height of the second and fourth cubes of the cubeoid (1, 2, 3, 4, 5 and 6); or at the height of the first and third cube in the cubeoid (7, 8, 9, 10, 11, 12, 14, 15, 16, 17, 18);
 61. The tetragonal prism of claim 59 wherein said tetragonal prism has one cube on a side of the cubeoid, said cube is placed at the height of the second cube in the cubeoid (19, 20, 21, 22, and 23).
 62. The tetragonal prism of claim 59 wherein the tetragonal prism has one cube on a side of the cubeoid at the height of the first cube (25 and 26).
 63. A process of manufacture for producing the three-dimensional construction game of claim 27, so that the resulting puzzle has both a desired form and interior three-dimensional puzzle pieces, comprising the steps of: a) selecting groups of pieces limited to those described in claims 60, 61, or 62, with repetition of pieces if necessary, b) assembling said pieces to obtain a desired form, for example, cube-shaped, staggered pyramid shaped, star shaped, or tetragonal prism shaped (FIG. 28); c) if necessary, cut the pieces of the resulting form into the precise outline of the desired three-dimensional object or figure so that cutting the periphery of the pieces of the object or figure reproduces a concrete area inside the surface of the shape and a concrete volume integrated in the total volume of the shape (depending on the place the piece takes up in the assembly). For example, to form a three-dimensional triangle one would cut the cube along the diagonal plane which intersects the cube's base and the cube's opposite top vertical edge (FIG. 30).
 64. The process of manufacture as described in claim 63 wherein the pieces that result from the process of cutting the object or figure are then used as the basis for producing copies of the resulting cut pieces (FIG. 29).
 65. The process of manufacture as described in claim 64 wherein the copies of the resulting cut puzzle pieces are made using machine tools.
 66. The process of manufacture as described in claim 64 wherein the copies of the resulting cut puzzle pieces are made using carpentry machinery.
 67. The process of manufacture as described in claim 64 wherein the copies of the resulting cut puzzle pieces are made using moulds 